Hi Rachel. We cruised with our son when he was 11 months old and again when he was 20 months old. Both times were to Bermuda.
Good plan on bringing your own pack and play. Not only are you assured taht you will have something that works, but it is both comfortable and familiar to your baby.
As to what to bring, the list is long, but probably not a whole lot different than if you were traveling anywhere. Bring more diapers than you think you'll need. Same goes for wipes. A small bottle of gentle laundry soap to use in the sink to rinse out his clothing. Scented diaper disposal bags. Any favorite baby food. Baby Tylenol and other medications. Sunscreen. A hat.
No need to request a high chair. They will have plenty on board.
As for dining, there will be a childrens menu in the main dining room. Be sure to order an appetizer for him -- even something like crackers or carrot sticks will do -- to be brought out the same time as your own appetizers. Otherwise, they'll serve his PB&J or pizza when you're on your own appetizer, and he'll be done well before your own entree arrives.
Milk and fruit are always available.
A stroller is great for roaming Bermuda. It is very easy to get around. St. George is a bit hilly, though, but still walkable. If you want to go anywhere beyond walking distance, I suggest a bus rather than taxi, unless you want to lug a car seat along.
As I think of anything else, I'll let you know. BTW, our son is now 13 years old and a self-professed cruise addict!
lol